霍金辐射多时关联中的佩奇相变
The Page Transition in the Multi-Time Correlations of Hawking Radiation
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中文总结 AI 辅助
该研究通过过程张量框架，揭示霍金辐射的佩奇相变可表现为辐射过程的马尔可夫阶相变，并利用纠缠楔重建和蒸发模型实现该机制。
中文摘要 AI 辅助
佩奇曲线和岛公式描述了霍金辐射中量子信息在佩奇时间前后的重组。我们研究了这种重组如何在多个延迟时间收集的辐射发射关联中显现。晚期辐射被视为一个协变多时过程，即过程张量，而 $\chi_{\mathrm{island}}=\mathcal{N}_{\varnothing}-\mathcal{N}_{R}$ 度量了当早期辐射寄存器 $R$ 被提供时被移除的时间记忆。在操作上，该量是辐射过程与马尔可夫参考过程的最优可区分性的相应变化。我们展示了蒸发过程，其单仓态和所有低于有限阶 $k_\ast\geq 3$ 的过程边缘分布保持固定，并与一个 CP 可分的参考过程一致，而 $\chi_{\mathrm{island}}$ 在 $k_\ast$ 阶发生一阶变化。因此，佩奇相变可以表现为辐射过程的马尔可夫阶的相变。当内部介导晚期时间记忆时，从 $R$ 对预测性内部进行纠缠楔重建使晚期过程马尔可夫化；相反，当晚期过程具有最小预测记忆且其影响未来的信息由该记忆介导时，通过 $R$ 的马尔可夫化提供了其影响的模拟器。一个 Hayden--Preskill 蒸发梳和一个蒸发 JT 计算实现了这一机制。晚期辐射在相变过程中保留时间记忆，而早期辐射变得足以预测其未来的多时统计。
英文摘要
The Page curve and the island formula describe a reorganization of quantum information in Hawking radiation across the Page time. We study how this reorganization appears in correlations among emissions collected at several retarded times. The late radiation is treated as a covariant multi-time process, or process tensor, and $χ_{\mathrm{island}}=\mathcal{N}_{\varnothing}-\mathcal{N}_{R}$ measures the temporal memory removed when the early radiation register $R$ is supplied. Operationally, this quantity is the corresponding change in the optimal distinguishability of the radiation process from a Markovian reference. We exhibit evaporation processes whose single-bin states and all process marginals below a finite order $k_\ast\geq 3$ remain fixed and coincide with a CP-divisible reference, while $χ_{\mathrm{island}}$ changes by order one at order $k_\ast$. The Page transition can therefore appear as a transition in the Markov order of the radiation process. When the interior mediates the late-time memory, entanglement-wedge reconstruction of the predictive interior from $R$ Markovianizes the late process; conversely, when the late process has a minimal predictive memory and its future-affecting information is mediated by that memory, Markovianization by $R$ supplies a simulator of its influence. A Hayden--Preskill evaporation comb and an evaporating-JT calculation realize this mechanism. The late radiation retains temporal memory across the transition, while the early radiation becomes sufficient for predicting its future multi-time statistics.
发表机构
- Department of Physics and Astronomy, University of Manchester（曼彻斯特大学物理与天文系）
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